blem #5: Suppose three tests are administered to a random sample of college students. Let X₁, Xy be observation vectors in R³ that list the three scores of each student, and for j = 1, 2, 3, let xj denote a student's score on the jth exam. Suppose the covariance matrix of the data is Problem #5: 10 20 23 80 44 53 S = 20 23 44 Let y = C₁x₁ + ₂x2 + Cc3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁0. Find the constants c₁,C₂, C3 so that the variance of y over the data set is as large as possible. Enter the values of c₁, C2, C3 into the answer box below, separated by commas. numbers correct to 2 decimals
blem #5: Suppose three tests are administered to a random sample of college students. Let X₁, Xy be observation vectors in R³ that list the three scores of each student, and for j = 1, 2, 3, let xj denote a student's score on the jth exam. Suppose the covariance matrix of the data is Problem #5: 10 20 23 80 44 53 S = 20 23 44 Let y = C₁x₁ + ₂x2 + Cc3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁0. Find the constants c₁,C₂, C3 so that the variance of y over the data set is as large as possible. Enter the values of c₁, C2, C3 into the answer box below, separated by commas. numbers correct to 2 decimals
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
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![Problem #5: Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be observation
vectors in R³ that list the three scores of each student, and for j = 1, 2, 3, let x; denote a student's score on the th
exam. Suppose the covariance matrix of the data is
Problem #5:
S =
10 20 23
20
80 44
23
44 53
Let y = 01x1 + 02x2 + c3x3 be an "index" of student performance with c + c3 + c3 = 1 and c₁ ≥ 0. Find the
constants C₁, C2, C3 so that the variance of y over the data set is as large as possible.
Enter the values of c₁, c2. c3 into the answer box below, separated by commas.
numbers correct to 2 decimals](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cb378ba-be87-4838-bd31-84fa6b2aaf1f%2Fcd10321d-a020-43d6-8115-d6bbe5c2e709%2F83lpdj_processed.png&w=3840&q=75)
Transcribed Image Text:Problem #5: Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be observation
vectors in R³ that list the three scores of each student, and for j = 1, 2, 3, let x; denote a student's score on the th
exam. Suppose the covariance matrix of the data is
Problem #5:
S =
10 20 23
20
80 44
23
44 53
Let y = 01x1 + 02x2 + c3x3 be an "index" of student performance with c + c3 + c3 = 1 and c₁ ≥ 0. Find the
constants C₁, C2, C3 so that the variance of y over the data set is as large as possible.
Enter the values of c₁, c2. c3 into the answer box below, separated by commas.
numbers correct to 2 decimals
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